@The Dude ouch, chasing hum. There are a lot of things out there to diagnose with much better results, but ... yeah.. gotta chase it down. I can only offer one suggestion here, which is shorting plugs. Make up a set of RCA plugs that are shorted (AT) the plug, as short as possible to the plug body. Using RCA barrels for cable testing, or just the plug at the amplifier inputs. Start at the amplifier, shorting the input and note the level of volume of hum on the volume knob, hopefully almost zero at full volume. Using the plugs with the barrels, one cable at a time one end plugged into that input, the other end shorting plug, note the level of him then on the volume control, again it "Should" be almost zero, but depending on the shielding there might be an increase. Once you know these things, then your source (CD, TAPE, DAC) plugged in to the same, and or through known cable of silence, if there is hum, then it may be within the source or the source cables. Now to make things more confusing, it is possible that is not the case, and just tuning the power cord around in the receptacle could make things better or worse. Opening the dreaded chase of ground loops. It sounds like you are speaking of the inclusion of a cable here increases the hum you hear, which may be shielding problems in that cable.
If you connect a cable to an input and just let it lay there open ended (no shorting plugs) you should get hum, as the cable is now acting like an antenna to the magnetic fields in your listening area. but shorting the cable should eliminate that hum unless the shielding is poor or broken. Keep in mind that a piece of equipment "IS" an antenna in itself, so the manufacturing engineering should have already resolved that with equipment grounding. I must talk safety here as well, since I suggest reversing the AC input to equipment, if it is 3 prong grounded then do NOT change that no matter what. Doing so "COULD" depending on what receptacles being used present 230 Volts between the 2 different sockets. (Opposed phase USA wiring for homes)
I have experienced using perfectly silent cables to hook up device cause terrible hum, and changing to a different cable reduces the hum, and that same cable that hums is perfectly silent on a different device. In that case it was the capacitance and inductance of that cable was not a good fit for the one device. So many things that will cause or solve the problem of hum. I wish you Luck and SUCCESS here in the chase. PM me if you wish and it shall be good to have the resolution posted here for others to ponder as they enter the chase.
Point of interest in this as I have been chasing down a hum here, and I finally found the source of the hum, and was not a cable (I thought it had to be one breaking down) but my cassette deck, just being plugged in was the cause, so the device will need repaired. This hum was being caused by old capacitors inside that are across the AC breaking down. I found this by a symptom of brushing my hand across the device I felt that famous electric buzzing.
I hope this is helpful and good luck!
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